On the relationship between minimum norm and linear prediction for spatial spectrum estimation

The minimum norm method for spatial spectrum estimation is derived from the linear prediction method in exactly the same way as the MUSIC method is derived from the minimum variance method. The derivation consists of replacing the correlation with its noise subspace component and setting all noise eigenvalues to unity. This makes it simpler to understand the methods and their properties. This relationship also brings out the meaning of setting the first element to unity in the minimum norm method — it corresponds to the predicted element in linear prediction. There is also a parallel between properties: e.g. just as linear prediction has a lower detection threshold than minimum variance so does minimum norm compared to MUSIC. Thus the properties of the subspace methods seem to be ’inherited’ from the original non-subspace methods.